Question

the expected value when you purchase a lottery ticket is - $2.00 and the cost of the ticket is $7.00. determine the fair price of the lottery ticket. the fair price is $ (simplify your answer. type an integer or a decimal.)

Explanation:

Step1: Recall the formula for expected value

The formula for expected value \(E(X)\) of a lottery ticket is \(E(X)=\text{Fair Price}-\text{Cost of ticket}\).

Step2: Rearrange the formula to solve for fair price

We can rewrite the formula as \(\text{Fair Price}=E(X)+\text{Cost of ticket}\).

Step3: Substitute the given values

Given \(E(X)= - 2\) and \(\text{Cost of ticket}=7\). Then \(\text{Fair Price}=-2 + 7\).

Step4: Calculate the result

\(-2+7 = 5\)

Answer:

\(5\)